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Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives. (Chinese) Zbl 1212.65342
Summary: A two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which modifies the well-known Darcy law. Using the relationship between Riemann-Liouville and Grünwald-Letnikov fractional derivatives, two modified alternating direction methods, a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence, of the two methods in a bounded domain are discussed. Finally, numerical results are given.
65M12Stability and convergence of numerical methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
65Z05Applications of numerical analysis to physics
76S05Flows in porous media; filtration; seepage